Question

Considerando log2 = 0,30 log3 = 0,47 e log5 = 0,70 determine o valor de log45
log 30 log2 15

Answer 1

log 45 = log(3².5)

log3² +log5

2log3 + log5

2(0,47) + 0,70

1,64

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log30 = log(2.3.5)

log2+log3+log5

0,30 + 0,47 + 0,70

1,47

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Answer 2

$\log_{}45=\log_{} 3^{2}.5=\log_{}3^{2} +\log_{}5= 2.\log_{}3 +\log_{}5=2.(0,47)+0,70$$=0,94+,070=1,64$

$\log_{}30=\log_{} 3.10=\log_{}3 +\log_{}10= 0,47 +1=1,47$

$\log_{2}15= \dfrac{\log_{}15}{\log_{}2} = \dfrac{\log_{}3.5}{\log_{}2} = \dfrac{\log_{}3+\log_{}5}{\log_{}2} = \dfrac{0,47+0,70}{0,30}$$= \dfrac{0,47+0,70}{0,30} = \dfrac{1,17}{0,30} =3,9$